The technique of performing a structural topology optimization was introduced in the early 1990s. Since then, after 10 more years of development, this technique has gradually become mature. Major differences between this structural topology optimization technique and the conventional structural shape parametric optimization are that the structural topology optimization technique can greatly enhance the structural performance and significantly change the shape. Broadly speaking, in a new design process of a machinery product, the initial step would be to introduce the technique of structural topology optimization to obtain an initial shape of the structure, then the optimization in shape and structural parameters would be applied to further modify detail scales, and thus an optimal structure for the machinery product can be reached.
Recently, people in designing machine tools have gradually tried to organize an initial structural configuration of a machine tool by performing the structural topology optimization. For example, in one of early applications, a typical task for minimizing the static compliance is executed by assuming the forcing on the structure is a static force. However, it is well known that the forcing on the tooling is always a dynamic force, or say an oscillating force. The assumption of static forcing in minimizing the static compliance can never be mapped to a dynamic response of the structure under oscillating forcing. Hence, researchers proposed to include a constraint condition of the nature frequency for better adjusting the structural dynamic characteristics. Moreover, a new assumption of treating the cutting force as a harmonic force was applied to achieve the dynamic compliance frequency response minimization. By providing the aforesaid design efforts, the static/dynamic stiffness of the design structure of the machine tool can be successfully improved. However, to the majority users of the machine tool, the static/dynamic stiffness is simple a relative abstract index that could probably means anything. It can be understood that the user of the machine tool expects to be taught if or not the machinability of the machine tool can meet his/her work requirement. Namely, the current structural topology optimization cannot provide a clear relationship between the structural characteristics (including static stiffness, nature frequency, dynamic stiffness and so on) and the machinability (including the maximum cutting depth and the like), and thus cannot directly perform the optimization upon the expected machinability of the machine tool.
On the other hand, the chatter analysis method in cutting is to transfer structural characteristics of the machine tool into cutting ability of the machine tool, so that a relationship between the structural characteristics and the cutting ability can be established. However, even though the conventional chatter analysis method in cutting can provide a meaningful relationship in between, the technique regarding how to improve the structure so as to upgrade the cutting ability is still yet to be developed. Further, in another effort, a technique that integrates the static stiffness topology optimization and the prediction of the cutting ability is actual an optimization process in static stiffness, not aimed to optimize the cutting ability. In particular, in this technique, the prediction of the cutting ability is appropriate to be executed after completion of the whole design process, and is simple for evaluation and prediction only.
From all the aforesaid techniques, since practical cutting action of the machine tool is dynamic, not static, thus the conventional efforts of applying structural topology optimization upon machine tools are restricted to analysis in static stiffness. The structural frequency response optimization for the cutting in a dynamic approach is yet to be achieved. Even that the structural topology optimization upon the dynamic stiffness of the machine tool structure can be introduced to improve the dynamic stiffness, following two problems are yet to be overcome.
(1) To designs, the optimized structure is still hard to be determined, and it is still in vague if the machinability can meet the designer's manufacturing requirements.
(2) Generally, a normal process for the structural topology optimization would never be applied to the amplitude with a negative real part. However, it is understood that the performance in cutting depth under chatter limits is highly related to that amplitude with a negative real part, and is unrelated to the amplitudes in other frequency domain.
In addition, if a cutting simulation for determining the machinability is performed after the design process of the machine tool structure is over, plenty of time would be wasted in repeating the modification of the structure if lack of machinability is found in the simulation.
Hence, if, in the early design stage of performing a structural topology optimization, the machinability is already raised as the topic of the design, then less error trials would be encountered in the following design process, and thus the design cycle would be greatly reduced.